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Speculative biomechanics
On the largest scale, the shape and the basic structure of organisms are dictated by two things: their function and mechanics. The size of a living being, the way organs and cavities are arranged inside the body, the way the parts of the skeleton interact are also the basis for any further speculation about its physiology. Body shape Cells and tissues Symmetry Symmetry is extremely important for the organization of the body: it provides a regular disposition of the bodyparts and often redundancy of limbs and organs. Most of pluricellular organisms on Earth show some form of symmetry, in four distinct degrees: *'Asymmetry' is very rare, at least between moving organisms, since it's a very inefficient way to organize the body and, if specialized organs are present, doesn't offer any reliable backup in the case of damage. Some primitive pluricellular organisms are completely asymmetrical, such as sponges and placozoans. *'Spherical symmetry': the organism can be divided in two specular halves by each of the three anatomical planes (sagittal, coronal and transverse, see image on the right). It's found in organisms that live in a 3-dimensional environment, submerged in a fluid dense enough to counteract gravity, and therefore they don't have any reason to privilege a specific direction: microscopic protozoans such as radiolarians, heliozoans and Volvox. *'Radial symmetry': the organism can be divided in specular halves by a number of planes (sagittal, coronal and possibly other) that pass through the dorsoventral axis. It's common among animals that live under the strain of gravity but motionless, and therefore distinguish only a dorsal side from a ventral one (eg., corals and sea anemones). The ventral side of a creature will produce possible limbs and will protect the most precious organs, such as the genitals, while the dorsal side will concentrate the passive defenses (shells, thorns, bony plates)There is at least an exception: the Triassic turtle Odontochelys had only a ventral armour, probably to defend itself when swimming on the surface of the sea.. With the exception of jellyfish, that move in the direction of their back anyway, radial animals never move much; the only bilateral animals subsequently turned radial are the echinoderms (e.g. sea urchins and starfish). Common forms of radial symmetry include: **''trimerism'' (body divided in three symmetrical parts) in some radiolars and in the extinct trilobozoans; **''tetramerism'' (four parts) in some jellyfish; **''hexamerism'' (six parts) and octamerism (eight parts) in corals (respectively Hexacorallia and Octocorallia); **''biradial symmetry'', used in the Ctenophora phylum: the body is divided in alternate quarters, each of which is different from the neighbouring ones but identical to the opposite one; **''pentamerism'' (five parts), the most common one: the symmetry axis are placed at 72° from each other. All the echinoderms show this symmetry, as well as many flowers and fruits, for example the petals of the dog rose and the seeds in an apple. **Radial flowers (such as the hexameric lily or the pentameric buttercup) are called actinomorphic. *'Bilateral symmetry': the organism can be divided in specular halves only by the sagittal plane. Animals that move in a specific direction rather than stay fixed on the ground/seafloor will develop an anterior extremity (a "head") that will meet first the new object and will interact with them. It will therefore contain a mouth, the main sense organs (and the central nervous system associated to them, if it exists), and perhaps simple manipulation organs such as tentacles. The right and the left side should remain specular, with few exceptions, since they have no reason to diversify: in fact, an asymmetry of limbs or muscles could cause the creature to move in circle rather than forward. Almost all animals on Earth, be they earthworms, wasps or turtles, are bilateral. Bilateral flowers, such as orchids and Lamiales, are called zygomorphic. *While most plants are asymmetrical on the whole, they often have branches or leaves arranged as a helix around the stem (helical growth); the cells of the Phycomyces fungi and the seaweed Nitella are helix-shaped, probably due to the arrangement of fibres in the cell wall. Note: some terms of location may be synonimous or meaningless depending on the shape and symmetry of the body (for example, human upright postur makes dorsal/ventral synonimous to anterior/posterior). Repetition and specialization In a primitive cell colony, different parts will tend to specialize to different functions, allowing them to maximize their efficiency - but they won't be able to survive on their own anymore, turning the colony in an organism. Ancestral organisms tend to have more repetition in their structure: ''Roulliet Law: The development of organisms, clades and other biological systems makes their organization more and more complex, with the differentiation and specialization of their sub-systems.'' ''Williston corollary: Organisms tend to have less limbs and segments (but more specialized) than their ancestors.'' Metamerism is the repetition of body segments with similar or identical structure, called somites or metameres in animals, and phytomers or metamers in plants (it's something different from mere segmentation, as in tapeworms, which is only a characteristic of external tissues). Annelids such as leeches and earthworms show homonomous metamery: all the segments are almost identical to the others, and they contain muscles, nephrids (excretion organs), part of the nervous chord and the digestive tract, a complete reproductive system and sometimes parapods (appendices without articulations). Arthropods are instead an example of heteronomous metamery, that typically arises from the specialization of homonomous metamery: each segment is very different from the others, and so are the limbs, that become legs, claws, chelicerae, palps and jaws. The head of insects, crustaceans and myriapods is made up by five fused segments, the head of trilobites and Chelicerata by seven; today, the body of insects appears composed by only three tagmata (head, thorax and abdomen), the body of many arachnids only by two (cephalothorax and abdomen); scorpions and crabs have a great cephalothorax and many abdominal segments, while mites appear to be entirely devoid of segmentation. Even when organs are specialized in function, they might have a very generic structure. Systems appear at first as a diffused net (of nerves, blood vessels, etc.) around the body, usually developing a greater centralization, with one or few main organs (brain(s), heart(s), etc.). The development "diffusion of chemicals from the environment" → "diffuse net that carries chemicals around the body" → "centralized system that controls the net" happens usually as a function of size (see the following paragraph). Furthermore, while an efficient design might require every function to be executed by an organ, the convoluted evolutionary story of living beings often cause an organ to execute many functions. For example, the pharynx of terrestrial vertebrates is both part of the digestive and respiratory system; jellyfish and flatworms eat and excrete waste through the same hole; sea cucumbers and turtles breath through the rectum, while the chinese soft-shelled turtle also urinates through the mouth; in reptiles and birds, the digestive, urinary and reproductive tracts all open in the cloaca. Conversely, organisms could execute the same function with different organs: squids have two hearts, octopuses have three, while ruminants have up to four stomachs. Finally, some organisms might forsake an organ completely: antlions don't have a stomach, because they eat only food digested by their enzimes outside their body, while many parasite worms don't have an intestine either, because they absorb only the nutrients already digested by the host. Volume and surface The relation between the volume and the surface of a solid is extremly important in several fields of biology. While the volume grows in proportion with the cube of the linear dimension, the surface grows in proportion only with the square, and therefore as a solid grows larger and larger its surface becomes (in relation to the volume) smaller and smaller: That means that very small organisms have a very large surface in relation to the volume. Since mass, weight and metabolic activity (of every part of the body, and the whole) are proportional to the volume, while surface areas and cross section are proportional to the surface, unicellular organisms can simply absorb the needed chemicals through the surface, and that's enough to sustain their processes; for larger organisms, the surface is too small, and they need complex systems to distribute the chemicals around the bodyparts. *Functions proportional to area: absorption of chemicals and light, heat dispersion, strength of muscle and bone, brain activity, amount of fluids delivered to the tissues, air/water friction, drag and lift *Functions proportional to volume: mass and weight, retention of heat, metabolic energy production, storage of chemicals, muscular power When a large-sized organism need functions proportional to a surface, it can increase its surface but not its volume through wrinkles, laminae, gyri, branches: pulmonary alveoli, intestinal villi, capillaries, leaves, gills are all structures that allow to efficiently absorb or release chemicals (or light, in the case of leaves) without unnecessay bulk. In the same way, brain gyri extend the thin cerebral cortex, and the mitochondria ridges permit a faster oxidation of glucose. Small organisms easily disperse heat - something very dangerous for small mammals and birds, that produce their own heat through metabolic activity, forcing them to stay much larger than cold-blooded animals - while large ones tend to retain it, and thus in a hot climate they need expanded surfaces, such as the ears of elephants. Another, more evident consequence is that as an organism increases in size it needs proportionally thicker and stouter supports: thus, elephants and sauropods have pillar-like limbs while insects and spiders walk on such thin legs. If a mouse is increased in size a hundred times from 5 cm to 5 m, it becomes 1003 = 1 000 000 times heavier, while its bones are only 1002 = 10 000 stronger: it's therefore a hundred times heavier than its skeleton can bear and it will need a radically different skeletal structure. Note: A pressure of 1 atm equals roughly the weigh of 1 kg, in Earth gravity, on each square centimetre. Many other peculiar features of small-scaled life are explained by the large area:volume ratio: *insects can carry loads hundreds of times heavier than them (while large mammals can carry only a fraction of their weight) since the cross-section of their muscles is much larger in relation to the muscles' mass; *as J.B.S. Haldane wrote, if a wet human has to carry a light film of water, a wet mouse has to carry its own weight in water, and a wet fly a mass of water many times heavier than its body; *many small animals can climb on vertical surfaces or walk on the surface of water, since at their scale the surface forces (e.g. surface tension) are much stronger than volume forces (e.g. weight); *insects can survive falls thousands of times higher than their body, while an elephant can fracture its bones by falling a few centimetres, since the force exerted by the fall depends only from mass and absolute height. Mass, gravity and proportions The most important stress that influences biomechanical structures is the pull of gravity. For example, the maximum height of an organism is given by the work of its structure to oppose its weight: E=mgh → h=E/mg. Since both E (the energy output) and m (the mass) are both proportional to the volume, they cancel each other out, and therefore the height is only inversely proportional to gravity: h ~ 1/g. That means that, if the gravity doubles, the maximum height of an organism in divided in half. The same is true for the maximum height reached by jumping: since it's independent from mass, a jerboa and a kangaroo jump roughly to the same height, but if the gravity increases n times, this height will become 1/n times greater (that is, smaller). Another consequence of changing gravity is the different burden upon the bones (or equivalent structures). The pressure the bones have to withstand is independent from the cross-sectional area, but it's directly proportional to weight, which is itself the product of mass and gravity: therefore, everything else being equal, the cross-sectional area of bones is directly proportional to gravity, and their radius to its square root (A ~ g, r ~ √g). If either the mass or the gravity double, the bones have to become √2 = 1.4 times wider. What are the lower and upper limits of size? The smallest known organism capable of metabolic activity (therefore excluding viruses) is the parasitic bacterium Mycoplasma genitalium, with a diameter of 200-300 nm and a mass of about 10-13 kg; the smallest organism able to survive on its own (therefore excluding parasites too) in Pelagibacter ubique, about 400 nm long. The smallest known eukaryote, that needs a cell much more complex that any bacterium, is the alga Ostreococcus, 800 nm wide. Finally, the smallest known animal is the crustacean Stygotantulus stocki, 0.094 mm long. Being eukaryotes, animals need cells much larger than the minimum size; it has been calculated that a human being built with Mycoplasma-sized cells would have a mass of 50 mg and a height of 5 mm, though it's unlikely that cells that small would be able to support complex life. As for the upper limit, largest sequoias, already built with a pillar-like shape, can weigh over 1000 tons, but they get to this size only because they don't have to move, something that puts much more stress on the structure; the largest known animals (blue whales and largest sauropods) have a mass of roughly 100 metric tons, or 105 kg. Perhaps on planets with weaker gravity the maximum mass would be higher: since mass is proportional to the cube of linear dimensions (such as height), and therefore to the cube of 1/g, we can deduce that the maximum mass is inversely proportional to the cube of gravity (m ~ 1/g3). The limits of relative gravity on inhabitable planets are believed to be 0.2 and 2.2: that would lead leading to maximum masses of 12500 tons and 9.4 tons, respectively. Anyway, since the support that whales get from buoyancy doesn't seem to affect the result much, it's likely that the limit to size is given by other factors, such as the retention of metabolic heat and the increasingly difficult blood circulation. Colonial organisms Usually, a colony is simply a group of organisms of the same species that live close to each other; a true colonial organism is a combination of joined cells that are still able to survive on their own: a likely evolutionary precursor of multicellular organisms. Volvox is an example of such a colony (called a coenobium, since it has a fixed number of unspecialized cells) composed by 500-50000 flagellate cells, hold together by a gelatinous matrix of glycoproteins. A biofilm is a group of microorganisms that adheres to a surface through a slimy mass of polysaccharides or other chemicals: it's an important source of food for many detritivorous organisms. There are examples of colonial organisms whose parts are in turn multicellular: they're called zoa (singular zoon) and the constituent individuals are called zooids. Zooids can be linked by soft tissue (as in corals and siphonophors) or share a common exoskeleton (as in pterobranchs and bryozoans). In some cases, mostly among siphonophors, of high specialization between zooids: for example, the "Portuguese man-o'-war" is composed by a pneumatophore (a translucid sac, 9-30 cm long, that floats on the surface of the sea), dactylozooids (tendrils up to 50 metres long, covered in stinging cells), gastrozooids (that digest killed preys) and gonozooids (that produce the sexual cells). This kind of association is rare on Earth, but on other planets it might be as common as simple multicellularity is here. Structure and protection Both static and mobile organisms will need rigid structures that oppose gravity allowing them to stand, and perhaps to move: the heaviest soft-bodied organism ever measured was a colossal squid (Mesonychoteuthis hamiltoni) weighing 500 kg, two hundreds times smaller than the 100 tons-limit to size given above, and without the support of water its maximum size would be even less. Boneless life has the advantage of flexibility - large octopuses can pass through holes a few centimeters wide (video), but a skeleton allows stability, protection and more efficient movement. Early skeletons The simplest form of skeleton is the hydrostatic skeleton, a cavity (coelom) or a system of cavities filled with liquid under pressure. Jellyfish, earthworms and starfish have such a system, that also works as muscle, providing both support and movement. Many animals have boneless mobile organs entirely composed of muscle (muscular hydrostats), such as the foot of mollusks (that becomes tentacles in cephalopods), the tube feet of echinoderms, the tongue of vertebrates and the trunk of elephants. Sponges have a rudimental skeleton composed by spicules, small mineral elements with 2-5 pointed extremities sprinkled in the tissue; they're made of calcite in calcareous sponges, silica in glass sponges and spongin (a protein) or both spongine and silica in demosponges. Echinoderms have a dermaskeleton, a simple rigid structure made up by calcite an magnesium oxide (MgO) plates, linked by the underlying and overlying layers of skin. A porous plate of madreporite filters seawater, which fills a net of canals, the water vascular system, with the triple function of locomotion, respiration and waste expulsion. Biomineralization Biomineralization is the process in which minerals are absorbed in the matrix of connective tissue to harden or stiffen it. Mineralized tissues include bone, horn, the enamel of teeth, shells and many others; their hollow structure make them 1000-10 000 stronger than the pure minerals. Earth lifeforms use: *'Calcite' is the most stable mineral form of calcium carbonate (CaCO3). It's part of the shell of many planktonic organisms (coccolithophores and foraminifera, that form deposits of chalk and limestone), brachiopods and bryozoans, and partially of bivalve mollusks, of the spicules of calcareous sponges and of the skeleton of tabulate corals. The eyes of the trilobites, unique among the animals, had calcite lenses. *'Aragonite' is another form of calcium carbonate (the third form, vaterite, is highly soluble in water, and it's therefore an unlikely replacement). It forms the shell of stony corals and all mollusks (though mixed with calcite in bivalves). Differently from calcite, it becomes unstable when magnesium becomes too rare in the environment relatively to calcium. *'Silica', or silicon dioxide (SiO2) forms the frustule (porous cells wall) of diatoms and some radiolarians and the spicules of glass sponges (see above). Many plants extract silica from the soil and store it in their tissues as phytoliths, which may have a structural function but mostly protect the leaves from grazing by wearing down the herbiores' teeth, especially in grass. *'Apatite' is a group of phosphate minerals, which include hydroxylapatite (Ca10(PO4)6OH2), fluorapatite (Ca10(PO4)6F2) and chlorapatite (Ca10(PO4)6Cl2). Depending on its concentration in the mineralized tissue, hydroxylapatite forms bone (50%, mixed with proteins), dentin (which is found in teeth and in fish scales, 70%) and tooth enamel (90%). In a process similar to biomineralization, some spiders and other arthropods accumulate solitary metal ions (mostly iron, copper, zinc and manganese) in their fangs, resulting in fangs that become progressively more metallic as the spider ages. While not common, such an adaptation could provide a definite advantage to the organism. Some tissues undergo a process analogue to biomineralization but with organis substances: tendon and cartilage contain proteins (collagen and elastin); another protein, keratin, forms hair, feathers, claws, nails, hooves, the sales of reptiles, the beak of birds and turtles, horn, the quills of porcupines and the armour of pangolins. Polysaccharides can be concentrated around each cell, building a cell wall with cellulose (and sometimes the complex lignin) in plants and chitin in fungi. External skeletons There are two ways of building a complex skeleton: the exoskeleton surrounds the soft tissues, while the endoskeleton is surrounded by them. The jointed exoskeleton is the hallmark of arthropods , in which case it's mostly made up of chitin, a polysaccharide, and permated by calcite: in insects it contains almost only chitin, while in trilobites, myriapods and crustaceans up to 40% of the exoskeleton is calcite. These substances form flexible jointed plates that cover all the body surface. It has internal projections, apodemes, on which muscles are hinged; being entirely composed of chitins, apodemes are six times stronger and twice as stiff as vertebrates' tendons. This kind of skeleton gives to muscles a much larger area available for attachment, and it's much more resistant to bending, but it has two issues which worsen with size: first, while it's true that a hollow beam is stronger than a solid one when sustaining static loads, it's much weaker when it comes to dynamic loading, that is, when walking or falling, if the animal's mass isn't very little; second, it hinders the animal's growth. This last issues has been solved by arthropods with periodic moulting, though extraterrestrial insects in which new tissues expands the same plates, or different layers of exoskeleton are alternately redeposited one around the other, can be imagined. Anyway, no terran arthropod, both on land and in water, has ever grown beyond 2-3 metres long. Less elaborate exoskeletons are found in other animals: brachiopods, bryozoans and some polychaete worms have one made up by calcite; mollusks have a distinctive dorsal tissue, the [http://en.wikipedia.org/wiki/Mantle_%28mollusc%29 mantle or pallium], which secretes calcium carbonate and conchiolin (a protein). It's a very hard shell, having a point of articulation only in bivalves, and in some brachiopods. A recently discovered gastropod, living in hydrotermal vents, has its aragonite shell reinforced by plates of iron sulphide, specifically greigite (Fe3S4) and pyrite (FeS2). Even some vertebrates have developed an exoskeleton: ostracoderm fish had a head armour of bone, cartilage and dentin, while turtles and armadillos have a bone carapace, and pangolins an armour composed by hair-derived keratin, which in other mammals also forms horns and quills. Category:Content Internal skeletons While the spicules of sponges, the echinoderm's dermaskeleton and the spongy aragonite cuttlebone of cuttlefish can be considered internal skeletons, a complex jointed endoskeleton is typical of chordates, in which is centered around a dorsal spinal cord, often a skull that protects the brain, a ribcage around the thoracic organs and protrusions that stiffen the limbs. This skeleton is composed either by cartilage (matrix or proteins, mostly collagen and elastin) or bone (ossein and calcium phosphate) with cartilage elements. Since bone can resist to a compression up to 1700 atm (that is, a weight equivalent to 1 kg on each square cm), that means that an animal with a mass of 5000 kg (assuming a gravity equal to Earth's) needs, at the very minimum, a total leg cross-section of 5000/1700=2.9 square centimetres, or, assuming one cylindrical leg, a bone diameter of 1.9 cm, while a cylindrical hardwood trunk (strength of 500 atm) should be 3.6 cm wide, a cartilage foot (strength of 350 atm) 4.2 cm wide, and a muscle foot (strength of 10 atm) 25 cm wide. Clearly, Earth's animals have much larger legs than this: that's because they're built not just for standing, but also for walking, running and leaping. When humans run, the foot strikes the ground with a force about 2.5 times larger than the body weight (the total force is therefore 3.5 times the weight), and in animals with less anatomical specialization for running it might be even higher. Putting all of this together, the formula to get the minimum legbone diameter is d = 2√(mgF/πnC), where m is the total body mass, g the relative gravity of the planet, F the magnitude of the total force relative to the body weight when running (we already got 3.5 for humans), n the number of legs and C the compressive strength of the bone. Let's assume 5000 kg of body mass again, Earth's gravity, F=4, six legs and true bone (1700 atm): we obtain thus legbones 2√(20000/32000) = 2√0.63 = 1.6 cm wide, for a total cross-section area of 12 square centimetres. An interesting variation of the endoskeleton is found in the basket skeleton (see halfway down here), a sort of "wicker basket" of interconnected bones that surrounds the soft body interior, similar to an enlarged version of the see urchin dermaskeleton or the hollow bones of birds; such a structure would combine great strength and lightness. Other alternatives proposed in Xenology include multiple spinal cords, helical ("corkscrew") arrangement of internal fibres, telescoping bones (one retracting inside another), etc. Category:Content Movement Muscle is a tissue composed by protein filaments; when they receive an electrical signal, they contract, shortening the muscle fibres and thus exterting a force. In arthropods, muscle are anchored on the internal surface of the exoskeleton, while in chordates they're tied to bones by tendons. Skeletal muscles are classified in four categories according to the arrangement of fibres: *In parallel muscles (e.g., the biceps brachii), fibres are all parallel to the longitudinal axis of the muscle. They can be flat or spindle-shaped, with tendons at both ends; they can contract up to two thirds of their maximum length, exerting a force of 36 N per square centimetre (3.6 atm). *In convergent muscles (e.g., the pectoralis major), fibres are spread from the attachment point, where a tendon or a similar structure is located. They're broad, flat and fan-shaped, and not as strong as parallel muscles, but they can pull in several different directions. *In pennate muscles (e.g., the extensor digitorum, unipennate, and the rectus femoris, bipennate), fibres form the same angle with the longitudinal axis (they're parallel to each other, but not to the tendon). They contain more fibres per unit of volume, and they're therefore stronger than other muscles. *In circular muscles or sphincters (e.g., the orbicularis oris), fibres are arranged in circle around a central aperture, restricting the diameter when they contract. They are often located around orifices and passageways to regulate the flow of matter. Locomotion Locomotion in a fluid Locomotion on a surface References *Extraterrestrial Biomechanics (Xenology) (also see further pages) *Mathematical Ideas in Biology (John Maynard Smith, 1968) *On Growth and Form (D'Arcy Wentworth Thompson, 1917) *Furahan Biology and Allied Matters (many reflections on the mechanics of posture and locomotion) Notes Category:Content